Stochastics and Probability

The main goal of the program is to develop high-quality research in a variety of areas that either involve stochastic phenomena or benefit from the application of stochastic techniques and insights. The broad lines of the program include probability theory, statistics, optimization, mathematical economics, ergodic theory and mathematical statistical mechanics. The program is particularly geared towards applications in other areas of mathematics and in issues of scientific or technological interest.

More specifically, some of the topics addressed in recent years by members of the group are: Combinatorial probability, random discrete structures, partitions, coagulation and fragmentation, regenerative combinatorial structures, Levy processes; optimal stopping, extreme values and records; asymptotic theory of statistical estimation, nonparametric curve estimation and Bayesian inference, adaptive estimation, estimation in time series and under censoring, stochastic approximation algorithms; game theory, economics, Young measures; beta expansions and transformations, applications of ergodic theory to number theory, probability theory and symbolic dynamics; long-memory stochastic processes, perfect simulation algorithms; non-Gibbsian and partially ordered specifications, cluster expansions and lattice boson models.

Operations Research

We also teach topics in operations research.